consider a market with inverse demand P(Q) = 10 − Q and two firms with cost curves C1(q1) = 2q1 and C2(q2) = 2q2 (that is, they have the same marginal costs and no fixed costs). They compete by choosing quantities. Suppose that Firm 1 chooses quantity first and is able to credibly commit to this choice. Then firm 2 choose its quantity after observing firm 1’s quantity. In the SPNE of this game, what is the price faced by consumers?- p = 3- p = 4- p = 5- p = 6- p = 7
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consider a market with inverse demand P(Q) = 10 − Q and two firms with cost
Suppose that Firm 1 chooses quantity first and is able to credibly commit to this choice. Then firm 2 choose its quantity after observing firm 1’s quantity. In the SPNE of this game, what is the price faced by consumers?
- p = 3
- p = 4
- p = 5
- p = 6
- p = 7
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- Here is a market with three firms: 1, 2, and 3. The demand curve is P=100-Q. There is no fixed cost but the marginal cost 10 for all firms. Firm 1 is a leader firm so that it decides the quantity Q1 first. Then two firms respectively decide their quantities Q2 and Q3 simultaneously. 1) At an equilibrium (SPE), Q1 is Q2=Q3= 2) At the equilibrium, (the market quantity) Q= and (the market price) P= 3) The profit of firm 1 is while the profit of firm 2 and 3 respectively isConsider two firms that produce the same product and sell it in a market with the following demand function: d(p) = max{0, 12 − p}, where p ≥ 0 is the unit price of the good. Suppose that, for technological reasons, firm 1 can produce either 4 units of output at the total cost of 10, or 6 units at the total cost of 15. Similarly, firm 2 can produce either 3 units of output at the total cost of 8, or 4 units at the total cost of 10. Assume that the firms make their production decisions simultaneously. Characterize the players’ strategy sets. Write down this game in the normal and extensive forms. Find all (if any) Nash equilibria of the game. Now assume that firm 1 makes its decision first. Firm 2 decides how much to produce after it observes firm 1’s output. Characterize the players’ strategy sets. Write down this game in the normal and extensive forms. Find all (if any) Nash equilibria of the game.Gamma and Zeta are the only two widget manufacturers in the world. Each firm has a cost function given by: C(q) = 10+20q + q^2, where q is number of widgets produced. The market demand for widgets is represented by the inverse demand equation: P = 200 - 2Q where Q = q1 + q2 is total output. Suppose that each firm maximizes its profits taking its rival's output as given (i.e. the firms behave as Cournot oligopolists). a) What will be the equilibrium quantity selected by each firm? What is the market price? What is the profit level for each firm? Equilibrium quantity for each firm__ price__ profit__ b) It occurs to the managers of Gamma and Zeta that they could do a lot better by colluding. If the two firms were to collude in a symmetric equilibrium, what would be the profit-maximizing choice of output for each firm? What is the industry price? What is the profit for each firm in this case? Equilibrium quantity for each firm__ price__ profit__ c) What minimum discount factor is required…
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